In an AP, (a_{3m}=94), (a_m=34), and (d=5). What is the value of (m)?
Answer and explanation
Correct answer: 6
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \,\(a_{3m}-a_m=(3m-m)d=2md\). Substituting the given values gives \,\(94-34=2m\times5\), so \,\(60=10m\). Hence, \,\(m=6\). If 5 were used, the difference between the terms would be only 50, so it is incorrect. Exam tip: In such questions, subtract the given terms instead of first finding the first term.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \,\(a_{3m}-a_m=(3m-m)d=2md\). Substituting the given values gives \,\(94-34=2m\times5\), so \,\(60=10m\). Hence, \,\(m=6\). If 5 were used, the difference between the terms would be only 50, so it is incorrect. Exam tip: In such questions, subtract the given terms instead of first finding the first term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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